FoldUnfold Table of Contents The Closure of a Set under Homeomorphisms on Topological Spaces The Closure of a Set under Homeomorphisms on Topological Spaces Recall from the Homeomorphisms on Topological Spaces page that if $X$ and $Y$ are topological spaces then a bijective map $f : X \to Y$ is said to be a homeomorphism if it is continuous and open. Furthermore, if such … [Read more...]

## The Interior of a Set under Homeomorphisms on Topological Spaces

FoldUnfold Table of Contents The Interior of a Set under Homeomorphisms on Topological Spaces The Interior of a Set under Homeomorphisms on Topological Spaces Recall from the Homeomorphisms on Topological Spaces page that if $X$ and $Y$ are topological spaces then a bijective map $f : X \to Y$ is said to be a homeomorphism if it is continuous and open. Furthermore, if … [Read more...]

## Homeomorphisms on Topological Spaces Examples 2

FoldUnfold Table of Contents Homeomorphisms on Topological Spaces Examples 2 Example 1 Homeomorphisms on Topological Spaces Examples 2 Recall from the Homeomorphisms on Topological Spaces page that if $X$ and $Y$ are topological spaces then a bijective map $f : X \to Y$ is said to be a homeomorphism of these two spaces if $f$ is also open and continuous, or equivalently, … [Read more...]

## Homeomorphisms on Topological Spaces Examples 1

FoldUnfold Table of Contents Homeomorphisms on Topological Spaces Examples 1 Example 1 Example 2 Homeomorphisms on Topological Spaces Examples 1 Recall from the Homeomorphisms on Topological Spaces page that if $X$ and $Y$ are topological spaces then a bijective map $f : X \to Y$ is said to be a homeomorphism of these two spaces if $f$ is also open and continuous, or … [Read more...]

## Homeomorphisms on Topological Spaces

FoldUnfold Table of Contents Homeomorphisms on Topological Spaces Homeomorphisms on Topological Spaces Recall from the Open and Closed Maps on Topological Spaces page that we said that if $X$ and $Y$ are topological spaces then a map $f : X \to Y$ is said to be an open map (or simply open) if for every open set $U$ of $X$ we have that $f(U)$ is open in $Y$. Similarly, $f$ … [Read more...]